produce nice latex code for latex(continued_fraction(pi)) and other continued fractions

[slabbe]

sage: latex(continued_fraction(pi))
\text{\texttt{[3;{ }7,{ }15,{ }1,{ }292,{ }1,{ }1,{ }1,{ }2,{ }1,{ }3,{ }1,{ }14,{ }2,{ }1,{ }1,{ }2,{ }2,{ }2,{ }2,{ }...]}}

[moritz]

I added a _latex_ function to the ContinuedFraction_base base class, that displays 10 terms by default. Notice that the subclass ContinuedFraction_periodic has already its own _latex_, printing all the terms.

---

New commits:

​54eef88

adding latex support for real continued fractions

[moritz]

(I hope my automatic white space correction didn't screw up the ascii-art to much..)

[vdelecroix]

Would be better to have only one place with _latex_. With your version we still have

sage: K.<sqrt2> = QuadraticField(2)
sage: continued_fraction(sqrt2)
[1; (2)*]
sage: latex(continued_fraction(sqrt2))
Traceback (most recent call last):
...
NotImplementedError: latex not implemented for non rational continued fractions

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

​0606ccd	added latex output to continued fraction of irrational algebraic numbers
​335bf30	Merge branch 'u/moritz/21928' of git://trac.sagemath.org/sage into u/moritz/ticket/21928

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

​a645dac

fixing old doctest and adding a new one

[slabbe]

Thanks for proposing a fix to this issue. I just downloaded the branch. It works great.

Here are two relatively small comments that I would suggest to change before positive review:

1. I think the nterms=10 would be better put as an argument with a default value of 10 for the _latex_ method like it is done for the method str of the same object. The first thing that will happen is that somebody want to see 13 terms (with the ...). I know that _latex_ method is used from latex function which might not forward arguments *args, **kwds. Something more complicated involving a new method could be done like ​here but I do not think it is necessary. To my opinion, I would just move nterms=10 to the argument which will allow somebody to see 13 terms (with the ...).

2. The two output lines in doctests are very long. I suggest to wrap them to keep less than 80 characters on each line. The doctest framework won't notice the newlines. Alternatively, the code could include well placed \n so that \frac{\displaystyle are all well aligned vertically.

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

​2765115

allow nterms as argmument and more line breaks

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

​d55256c

removed one line

[moritz]

I addressed both points mentioned by slabbe; thanks for reviewing!

[slabbe]

sage -grep continued_fraction lists 20 files and sage -tp --long on them gives all tests passed:

sage -tp --long src/sage/arith/misc.py src/sage/calculus/wester.py src/sage/combinat/words/word_generators.py src/sage/databases/oeis.py src/sage/geometry/cone.py src/sage/modular/modform_hecketriangle/hecke_triangle_group_element.py src/sage/modular/modform_hecketriangle/hecke_triangle_groups.py src/sage/modular/modform_hecketriangle/readme.py src/sage/modular/modsym/ambient.py src/sage/modular/modsym/modular_symbols.py src/sage/modular/pollack_stevens/manin_map.py src/sage/plot/misc.py src/sage/rings/all.py src/sage/rings/contfrac.py src/sage/rings/continued_fraction.py src/sage/rings/number_field/number_field_element_quadratic.pyx src/sage/rings/rational.pyx src/sage/rings/real_lazy.pyx src/sage/tests/book_stein_ent.py src/sage/tests/book_stein_modform.py

I am currently building the documentation to make sure...

[chapoton]

in the future, remember to use python3 syntax for print